Fuzzy Relational Model Research Articles

Counterfactuals in fuzzy relational models

Given the pressing need for explainability in Machine Learning systems, the studies on counterfactual explanations have gained significant interest. This research delves into this timely problem cast in a unique context of relational systems described by fuzzy relational equations. We develop a comprehensive solution to the counterfactual problems encountered in this setting, which is a novel contribution to the field. An underlying optimization problem is formulated, and its gradient-based solution is constructed. We demonstrate that the non-uniqueness of the derived solution is conveniently formalized and quantified by admitting a result coming in the form of information granules of a higher type, namely type-2 or interval-valued fuzzy set. The construction of the solution in this format is realized by invoking the principle of justifiable granularity, another innovative aspect of our research. We also discuss ways of designing fuzzy relations and elaborate on methods of carrying out counterfactual explanations in rule-based models. Illustrative examples are included to present the performance of the method and interpret the obtained results.

RELATIONAL-SEPARABLE MODELS OF MONITORING PROCESSES WITH VARIABLE AND FUZZY OBSERVATION INTERVALS

The report presents the results of research on the formation of models and procedures intended for the analysis and forecasting of the characteristics of non-deterministic processes represented by time sequences with uneven and fuzzy interval models (UFMI) between observations. At the same time, the data of monitoring processes of rehabilitation of patients, maintenance of systems according to the current state, etc. were used. at UFMI. The development of fuzzy relational and combined relational-separable models (RSM) of the first and second order, intended for the analysis and forecasting of sequences of UFMI data, was carried out. The possibility of increasing the accuracy and numerical efficiency of the modeling of the specified monitoring processes when applying RSM algorithms has been established.

EVALUATION OF THE INFLUENCE OF ENVIRONMENTAL FACTORS AND COGNITIVE PARAMETERS ON THE DECISION-MAKING PROCESS IN HUMAN-MACHINE SYSTEMS OF CRITICAL APPLICATION

Context. A feature of human-machine systems of critical application operating in real time is that they include as elements both technical systems and people interacting with these systems. At the same time, the main difficulties are associated not only with the improvement of hardware and software, but also with the insufficient development of methods for reliably predicting the impact of the production environment on the human factor and, as a result, on the relevance of decisions made by decision makers. As a result, the task of developing methods for determining the mutual influence of environmental factors and cognitive parameters of decision makers on the decision-making process becomes very relevant.
 Objective. The aim of the work is to propose methodological foundations for the development and study of fuzzy hierarchical relational cognitive models to determine the influence of environmental factors and cognitive parameters of decision makers on the DMP.
 Method. When building FHRCM methods of “soft computing”, methodologies of cognitive and fuzzy cognitive modeling were used, providing an acceptable formalization uncertainty of mutual influence of factors on the DMP.
 Results. A fuzzy cognitive model based on a fuzzy Bayesian belief network has been developed, which makes it possible to draw a connection between qualitative and quantitative assessments of mutually influencing factors on the DMP. The proposed model makes it possible to probabilistically predict the influence of factors and choose rational ways of their interaction in the DMP.
 Conclusions. The results of the experiments make it possible to recommend using the developed model, which takes into account the mutual influence of factors of various nature, including cognitive ones, in the DMP in order to improve the efficiency of HMSCA management as a whole.

An Extended Type-2 Fuzzy Relational Database Model for Aggregate and Grouping Operations

This paper introduces an extended type-2 fuzzy relational database model (ET-2FRDB) for aggregate and grouping operations that can represent and query uncertain and imprecise information in the real world applications. In ET-2FRDB, each fuzzy relation is represented by a type-2 fuzzy set whose membership degree of each tuple is a fuzzy number on [0, 1], the fuzzy aggregate functions, the fuzzy relational algebraic, aggregate and grouping operations are defined as extensions of those in the classical relational database model thereby the membership degree of tuples associated by using the minimum and maximum of fuzzy numbers. Also, some properties of the fuzzy relational algebraic, aggregate and grouping operations in ET-2FRDB are formulated and proven.

G-normal fuzzy relational models are universal approximators

Making a fuzzy relational model (FRM) g-normal by a specific configuration of the FRM and putting some constraints on both its fuzzifier and its fuzzy relational matrix, results in some favorite features at the expense of loosing some degrees of freedom. In this paper, we show that the g-normal fuzzy relational modeling structure has the universal approximation property despite all the constraints that makes the model g-normal. Indeed, we prove that any real function in Lp (including continuous functions) can be modeled by a g-normal model with any arbitrary accuracy when the universe of discourse is a compact set.

Research on uncertain multiple attribute decision making based on improved possibility degree relation model and its application

In this paper, we mainly focus on the triangular fuzzy number-based uncertain multiple attribute decision making problem, which not only attribute weights are unknown but also preference for decision-making objects do not exist, and give a new decision-making approach and consistency test method based on the improved possibility relation model. This method fully considers the influence of the comparison possibility degree measurement information between the measured values of the indicator attribute itself in the course of processing uncertain reasoning such as fuzziness and randomness, reconstructs a new and more optimized triangular fuzzy number-based decision making object improved possibility degree relation model (TFN-DMOIPDRM) to determine the attribute weight vector, and creatively designs a general formula to test the consistency of the improved possibility degree relation matrix. Next the criterion of consistency test is given to solve the remaining problem of the lack of consistency test in the construction of fuzzy number possibility degree relation model and fuzzy complementary judgment matrix. Moreover, another major contribution of this paper is to present the improved possibility degree relation theory of triangular fuzzy numbers on the basis of defining the comparative possibility degree of triangular fuzzy numbers, and fully study a series of its relevant properties and conclusions, as well as its application in constructing model to determine the attribute weight. By aggregating the improved possibility degree information measured by pairwise comparing decision objects, the overall improved possibility degree value of each decision object is obtained, and a new algorithm of the improved possibility relation model for triangular fuzzy number multi-attribute decision object is given, which improves and expands the application of fuzzy number possibility theory in the field of fuzzy uncertainty reasoning and intelligent computing of artificial intelligence.

Development of a method of complex analysis and multidimensional forecasting of the state of intelligence objects

A method of complex analysis and multidimensional forecasting of the state of intelligence objects is proposed to increase the accuracy of their state assessment. The object of research is decision support systems. The subject of research is the process of decision-making in management problems using artificial intelligence methods. The hypothesis of research is to increase the efficiency of decision-making with a given assessment reliability. The proposed method is based on a combination of fuzzy cognitive and temporal models, an advanced cat swarm optimization algorithm and evolving artificial neural networks. The method has the following sequence of actions: ‒ input of initial data; ‒ processing of initial data taking into account uncertainty about the state of heterogeneous intelligence objects; ‒ construction of a fuzzy temporal ontological model of heterogeneous intelligence objects; ‒ conclusion on the state of heterogeneous intelligence objects; ‒ correction of the fuzzy temporal ontological model; ‒ building a fuzzy relational temporal cognitive model of heterogeneous intelligence objects and forecasting the state of the intelligence object; ‒ training knowledge bases on heterogeneous intelligence objects. The training procedure consists in learning the synaptic weights of the artificial neural network, the type and parameters of the membership function, as well as the architecture of individual elements and the architecture of the artificial neural network as a whole. The method makes it possible to increase the efficiency of data processing at the level of 18–25 % by using additional improved procedures. The proposed method should be used to solve the problems of evaluating complex and dynamic heterogeneous intelligence objects, characterized by a high degree of complexity.

Ranking Method of Intuitionistic Fuzzy Numbers and Multiple Attribute Decision Making Based on the Probabilistic Dominance Relationship

The uncertainty of intuitionistic fuzzy numbers (IFNs) is further enhanced by the existence of the degree of hesitation (DH). The shortcomings of existing researches are mainly reflected in the following situations: when comparing IFNs, the comparison rules of IFNs are difficult to apply to the comparison of any two IFNs, or the relevant methods do not fully consider the uncertainty expressed by DH. Thus, the rationality of the decision results needs to be improved. On the other hand, multi-attribute decision making (DADM) based on IFNs is often not objective due to the need to determine the attribute weight. Moreover, the strict condition of attribute aggregation of classical dominance relation makes it a method that fails considering the practical application. Aiming at the comparison problem of IFNs, this paper takes probability conversion as the starting point and proposes an IFN comparison method based on the area method, which can better deal with the comparison problem of “either superior or inferior” IFNs. In addition, aiming at the MADM problem of an intuitionistic fuzzy information system, we propose an intuitionistic fuzzy probabilistic dominance relation model and construct the MADM method under the probabilistic dominance relation. The series properties of IFNs and probabilistic dominance relation were summarized and proved, which theoretically ensured the scientificity and rigor of the method. The results show that the comparison and ranking method of IFNs proposed in this paper can be applied to the comparison of any two IFNs, and the dominance degree of IFNs is presented in the form of probability, which is more flexible and practical than the classical method. The probabilistic dominance relation method based on IFNs avoids the problem of determining attribute weights subjectively or objectively, and the decision maker can reflect decision preference by adjusting decision parameters to better match the actual problem. The application of this model to a campus express site evaluation further verifies the feasibility of the proposed method and the rationality of the results. In addition, various extension problems of the model and method proposed in this paper are discussed, which pave the way for future related research. This paper constructs a complete decision-making framework through theoretical analysis and application from practical problems, which provides a reference for enriching and improving uncertain decision-making theory and the MADM method.

A g-Normal fuzzy relational hybrid model based control design for hybrid systems with continuous-valued inputs

In this paper, the indirect adaptive control of a special class of hybrid systems is proposed. The proposed control scheme is based on g-normal fuzzy relational hybrid models (g-Normal FRHMs) in which the model of both plant and controller are proposed to be modeled by FRHM structure. There is an assumption on control action to be of continuous-valued type. In order to design a control scheme for both regulation and reference tracking, an additional simplifying assumption is considered. Indeed, when the tuning mechanism is extracted, it is assumed that the defuzzifier of the controller’s model and the fuzzifier of the plant’s model are approximately inverse of each other and can be simplified. The proposed control approach is then applied to a DC-DC buck converter as our case study. The simulation results show that the proposed adaptive control based on g-Normal FRHM can regulate and also track the reference input in the presence of both load and supply voltage disturbance.

Fuzzy relational representation, modeling and interpretation of temporal data

In virtue of omnipresence of temporal data (time series), a quest for efficient and interpretable models of such data becomes of paramount relevance. The accuracy-interpretable dilemma becomes more visible in light of the current trend of producing accurate, yet comprehensible models supporting users in making sound and highly actionable conclusions. This study is positioned in the realm of human-centric granular representation of temporal data (time series) where the logic settings of relational calculus is realized at the level of information granules. We establish modeling pursuits and resulting constructs at a certain level of abstraction delivered by information granules expressed as fuzzy sets. While have been some studies involving a framework of granular computing applied to granular models of time series, in this study we advocate a unified and original environment of logic blueprint of relational dependencies among information granules articulated by means of weighted logic expressions where both the components of the expressions as well as their associations are quantified (calibrated) in the presence of available experimental data. An overall processing scheme is structured as the following sequence of main functional modules: granulation (encoding) – relational computing – logic interpretation – numeric characterization of results (produced through decoding). Relational computing engages a suite of architectures that capture temporal dependencies describing predictions at the level of granular amplitudes and granular trends. The quality of the relational model is quantified at the level of information granules (which emphasizes the interpretability aspect) as well as. A series of experiments is reported to demonstrate the performance of the relational models and their performance impacted by the parameters of the relational architectures.

A relational database model and algebra integrating fuzzy attributes and probabilistic tuples

Although there have been many fuzzy or probabilistic relational database models proposed for representing and handling imprecise and uncertain information of objects in real-world applications, models combining the relevance and strength of both fuzzy set theory and probability theory appear sporadic. In this paper, we propose a new fuzzy and probabilistic relational database model where the imprecision of an attribute value is represented by a fuzzy set and the uncertainty of a relational tuple is represented by a probability interval. The mass assignment theory is employed to deal with the challenge of integration and computation of both fuzzy sets and probabilities in the same model. The conjunction and disjunction strategies to combine imprecise and uncertain information are introduced. Then the fundamental concepts of the classical relational database model are extended and generalized in this new model. The syntax and semantics of the selection operation are formally defined. Finally, the other important algebraic operations on imprecise attributes and uncertain tuples are developed.

Using fuzzy relational hybrid models to control mixed‐valued dynamic systems with discrete‐valued inputs

This is the first attempt to bring the fuzzy relational hybrid models from modelling to control. The main challenge is to configure both the plant model and the controller appropriately so that the overall system has good analytical and numerical properties. However, to close the control loop effectively by connecting the fuzzy relational hybrid model blocks, it is needed for its core mathematical operator to be associative. Therefore, in this paper: (1) It has been shown that the core mathematical operator that relates the connected g-normal fuzzy relational hybrid model blocks, that is, the Yager-product fuzzy relational inner composition, unlike most fuzzy relational inner compositions, is associative; (2) An intelligent adaptive control scheme has been developed for a class of plants in which the states of the system can be mixed-valued and all inputs are of discrete-valued type (either quantitative or qualitative). Benefiting from the associative property, the proposed control scheme uses the g-normal fuzzy relational hybrid model building blocks in the role of the controller as well as the plant model with no prior knowledge of the elements of the fuzzy relational matrices. Being applied to control a synchronous buck converter in both regulation and tracking scenarios, and under parameters uncertainties, the proposed scheme has been evaluated by computer simulation.

Natural Computing of Human Facial Emotion Using Multi-Learning Fuzzy Approach

Emotions are described as strong feelings that are expressed by an individual in response to reactions to something or someone. Emotions are a very important aspect of day-to-day life interaction. Research shows that more than 90% of communication will happen non-verbally. This paper presents human emotion detection using a fuzzy relational model. The model consists of an image processing stage followed by an emotion recognition phase. The authors additionally made sub-categories in the most important expressions like happy and sad to discover the level of happiness and sadness in one face. Feature extraction along with multi-learning approach will help to test whether the person is truly happy or appearing to be happy. Experimental outcomes on the image dataset point out the accurate performance of the proposed technique. The experiment gives good accuracy results with the authors' own data set and robust with reference to some latest and leading edge.

FUZZY RELATIONAL DATABASE MODEL AND MANAGEMANT SYSTEM FOR IMPRECISE INFORMATION

This paper introduces a fuzzy relational database model (FRDB) and the management system for it. FRDB is built by extending the classical relational database model with the fuzzy membership degree of tuples in relations. The management system for FRDB with the querying language like SQL is built by using a classical open-source management system.

Fuzzy cognitive modeling of heterogeneous electromechanical systems

The article presents a method of fuzzy cognitive modeling for heterogeneous electromechanical systems (HEMSs) in the management of innovative design solutions. During the operation of the HEMSs, as a result of their operational aging, the properties of the windings parametric matrices and the HEMSs vector space properties change. Periodic testing of the HEMSs vector space allows obtaining reliable information about the current technical condition of the HEMSs, about its changes during operation and about the risks of operating capability loss. At the same time (I) the presence of proportional changes in signals during sequential testing indicates the homogeneous operational aging of the HEMSs and its rate; (II) a disproportionate change in one of the signals indicates the damage or the development of a heterogeneous aging process; (III) a change in signals with a change in the angular position of the rotor indicates worn bearings or damage of the HEMSs rotor. The article presents the HEMSs model, describes the method for the topological research of the vector space and the method for forming the diagnostic matrices. The deviations of their elements are fuzzy due to the uncertainty of the load, influencing environmental factors and unstable supply voltages. Therefore, for predictive estimation of the HEMSs state, it is proposed to use fuzzy relational cognitive models that allow implementing a completely fuzzy approach to modeling problem situations in these systems. The presented data confirm the growth of the HEMSs heterogeneity under conditions of uncertainty of external influences. The proposed method for predictive estimation of the HEMSs state, based on fuzzy relational cognitive models, provides resistance to an increase in the uncertainty of the estimation results for various models of system dynamics due to a reasonable set of fuzzy vector-matrix operations.

Network-based evidential three-way theoretic model for large-scale group decision analysis

Social relationships are critical to the group decision-making (GDM) process, especially for large-scale scenarios. Conventional GDM models have several drawbacks when applied to large-scale GDM problems. In this paper, we propose an evidential three-way theoretic model for large-scale group decision analysis based on the introduction of ego networks. A similarity matrix of all individuals is obtained after ego network generation via social network feature extraction. Rough and smooth detection are then conducted in the framework of three-way decisions. Specifically, the degree of organizational influence is analyzed based on the generated basic probability assignments (BPAs), and the individuals are divided into several organizations. After an opinion collection process, preference evolution is implemented via a social influence network (SIN) technique and a fuzzy preference relation (FPR) model. Then, the global final scores of all the alternatives are obtained using an aggregation process. Finally, we conduct a simulation experiment to illustrate the entire procedure. Based on a comparison of related methods, we believe that the proposed method can reasonably solve real-world large-scale group decision-making (LSGDM) problems and has good practicability and effectiveness.

THE PRINCIPLES OF DEVELOPING A MANAGEMENT DECISION SUPPORT SYSTEM FOR SCIENTIFIC EMPLOYEES

Employees engaged in mental work have become the most valuable assets of any organization in the 21st century. The satisfaction of those involved in mental work requires the provision of objectivity and transparency in their decision-making. This, in turn, entails the development of scientifically motivated decision making mechanisms and scientific-methodological approaches to evaluate their performance based on innovative technologies. The main goal of this article is in development of the scientific and methodological framework for the establishment of a decision support system to manage the employees engaged in mental work and operating in uncertainty. In this regard, initially, the question of evaluating the activities of scientific workers is examined, its characteristic features are determined, and the fuzzy relation model is proposed as a multi-criterion issue formed in uncertainty. Taking into consideration the hierarchical structure of the criteria that allows evaluating the activities of scientific workers, a phased solution method based on an additive aggregation method is proposed. In accordance with the methodology, a functional scheme of the decision support system to manage the scientific personnel is developed. The working principle of each block and the interaction of the blocks are described. The rules for the employees’ management decisions are shown by referring to the knowledge production model. Based on the proposed methodological approach, the implementation phases of the decision support system for the management of the scientific workers of the Institute of Information Technology of ANAS are described. To evaluate the employees’ performance, the tools to collect initial information, evaluate the system of criteria, define their importance coefficients and mathematical descriptions are provided. Some results of the system software are presented. The opportunities of the system based on the proposed methodology to support enterprise mangers to make scientifically justified decisions are provided.

Fuzzy Relational Model to Establish Credit Worthiness of Sacco Members in Kenya

Fuzzy Relational Model to Establish Credit Worthiness of Sacco Members in Kenya

A fuzzy causal relational mapping and rough set-based model for context-specific human error rate estimation

Safety is of paramount importance in high-risk systems. Safe and reliable operation of a system depends mainly on its key component, ‘the human’. Human error is pivotal in an accident sequence and the rate of error is instrumental in the analysis of accidents which focuses on the development of interventions. However, assessing the rate of human error is a big challenge. Human performance and the rate of error are governed by the context of work. This study discusses a fuzzy rule-based causal relational mapping approach to investigate the variability of the human error rate with context. Different contexts are mapped onto the human error rate estimated from the reported accident cases. This mapping develops a causal relational diagram which can be used for predicting the human error rate in any context. Such information is useful to identify problems of areas and to develop safety countermeasures.

An Innovative Rough Set Model based on Fuzzy Covering for Ordered Decision Making

Fuzzy and rough sets are considered to be complementary to each other, addressing different aspects of uncertainty and vagueness. The rough set theory has been extended and modified such that it can be applied to the preference analysis in ordered decision making. However, neither the ordered structure nor dominance degrees among the investigated objects can be revealed during the ordered decision making process. In this paper, an innovative rough set model based on fuzzy covering is developed for ordered decision making. First, the crisp preference relation rough set model and the fuzzy preference relation model for ordered decision making were introduced. Next we integrated the fuzzy preference relation with the crisp preference relation rough set model to propose an innovative rough set model based on fuzzy covering for ordered decision making. Using the innovative model, both the ordered structure and dominance degrees among the investigated objects can be revealed during the ordered decision making process. The proposed model was then compared with the crisp preference rough set model. Finally, the proposed model is utilized to analyze fuzzy preference data obtained from real experiments of ordered decision making. Results validated the effectiveness of the innovative model.